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I want to write a script that reads an input text file that specifies the parameters and then uses them to solve an integral

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Gideon Sarpong
Gideon Sarpong 2022-12-14
回答： Fabio Freschi 2022-12-16
I want to write a script that reads an input text file that specifies the parameters:
a:1
b:2
c:3
d:4
x0:1
y0:1
tf:25.
Then integrate a system of equations given the parameters read from the input text file. Sytem should be integrated from t=0 to t=tf. After plot x(t) and y(t) in a single graph.
This is what I did. It gives me errors. Kindly tell me what i am doing wrong and how to solve the question. Thanks.
[q,w] = readvars('variables.txt');
a = w(1);
b = w(2);
c = w(3);
d = w(4);
x0 = w(5);
y0 = w(6);
tf = w(7);
t = 0;
x = linspace(t,tf,25);
fx = @(x,y) a*x-b*x*y;
fy = @(y,x) c*x*y-d*y;
x = linspace(t,tf,25);
for i = 1:length(x)
fx(i)= integral(@(x)(fx(x,y)),t,x(i));
end
y = linspace(t,tf,25);
for k = 1:length(y)
fy(k)= integral(@(y)(fy(y,x)),t,y(k));
end
figure (1)
plot(fx)
plot(fy)
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显示 1更早的评论
Gideon Sarpong
Gideon Sarpong 2022-12-14
Ran in:
I improved the code to this and i do not get errors but shows this plot.
[q,w] = readvars('variables.txt');
a = w(1);
b = w(2);
c = w(3);
d = w(4);
x0 = w(5);
y0 = w(6);
tf = w(7);
t = 0;
a = w(1);
b = w(2);
y = 0.5;
fx = @(x) a*x-b*x*y;
format long
fx = integral(fx,t,tf,'RelTol',1e-8,'AbsTol',1e-13,'ArrayValued',true);
c = w(3);
d = w(4);
x = 4/3;
fy = @(y) c*x*y-d*y;
format long
fy = integral(fy,t,tf,'RelTol',1e-8,'AbsTol',1e-13,'ArrayValued',true);
figure (1)
plot(fx,'*')
hold on
plot(fy)
Torsten
Torsten 2022-12-14
I can only repeat: you can't use "integral" to solve differential equations that depend in the dependent variable.
You must use one of the ode integrators or try "dsolve".

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采纳的回答

Fabio Freschi
Fabio Freschi 2022-12-16
Ran in:
As suggested by @Torsten your problem is a system of first order ODEs and you must use a ODE integrator. Try this
clear variables, close all
% your params (you can instead load here your file)
a = 1;
b = 2;
c = 3;
d = 4;
x0 = 1;
y0 = 1;
tf = 25;
% define the system of ODE as anonymous function.
% The vector variable is here X, with X(1) = x, X(2) = y
odeFun = @(t,X)[a*X(1)-b*X(1)*X(2); c*X(1)*X(2)-d*X(2)];
% initial value
X0 = [x0; y0];
% time interval
tSpan = [0 tf];
% solution with ODE45
[t,X] = ode45(odeFun,tSpan,X0);
figure
plot(t,X)
xlabel('time');
legend('x','y')

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